Lunch break on 8 hour day CA

When I was originally hired I was promised 30 hours a week. As slow times approached my hours were cut down to 28 a week. Some how my supervisor did not realise this and when I mentioned it she said I wouldn't have to clock out for lunches on 2 of my shifts. (Which still only put me at 29 hours but I didn't say anything.) Weeks later on one of the days I was told not to clock out for lunch I came back to find my superviser there, upset because I left. She claims she thought I was working 8 straight hours without a lunch. My question is, is it legal to force an employee to work 8 hours without a lunch?

As I understand state law in California, no, it isn't. My understanding is that if you are non-exempt, your employer is required by law to give you a 10 minute rest break for every four hours that you work, and a 30 minute meal break within five hours of starting work, as long as you work 6 hours total or more. There are a few industry-specific exceptions for the motion picture, household, and agricultural industries.

I'm not 100% certain if the same applies if you are exempt. In many states, breaks are only mandatory for non-exempts; I don't know for sure if CA is one of them. Lillian?